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Diffraction by a three‐dimensional lattice

Dennis Sherwood and Jon Cooper

in Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199559046
eISBN:
9780191595028
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199559046.003.0008
Subject:
Physics, Crystallography: Physics

This chapter describes the basis of X-ray diffraction by a three-dimensional crystal and introduces the Laue equations which describe the geometric conditions for constructive interference of X-rays ... More


DETERMINATION OF THE SUPERSPACE GROUP

Sander Van Smaalen

in Incommensurate Crystallography

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198570820
eISBN:
9780191718762
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570820.003.0009
Subject:
Physics, Crystallography: Physics

This chapter presents the steps that are required to determine the superspace group of an aperiodic crystal from its diffraction pattern. This includes the analysis of the metric of the reciprocal ... More


Introduction to diffraction

Peter Main

in Crystal Structure Analysis: Principles and Practice

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199219469
eISBN:
9780191722516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219469.003.0001
Subject:
Physics, Crystallography: Physics

This introductory chapter provides information on some fundamental aspects of crystal structures and their diffraction of X-rays as a basis for the rest of the book. It describes electrons, atoms, ... More


The reciprocal lattice

Christopher Hammond

in The Basics of Crystallography and Diffraction

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198738671
eISBN:
9780191801938
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198738671.003.0006
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

Chapter 6 starts by looking at some basic concepts: representation of a family of lattice planes by a reciprocal lattice vector—leading to reciprocal lattices and unit cells. It then considers the ... More


Crystallographic computing

Carmelo Giacovazzo

in Fundamentals of Crystallography

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199573653
eISBN:
9780191775000
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573653.003.0002
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

This chapter describes the fundamentals of crystallographic computing. Among the various topics available, those that are of more frequent use have been selected: axis transformations and geometric ... More


Fundamental crystallography

Xiaodong Zou, Sven Hovmöller, and Peter Oleynikov

in Electron Crystallography: Electron Microscopy and Electron Diffraction

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199580200
eISBN:
9780191731211
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199580200.003.0002
Subject:
Physics, Crystallography: Physics

The basic concepts of crystallography, including unit cell, symmetry, crystal systems and origin specification are introduced. Bravais lattice, point groups, plane groups and space groups are ... More


Symmetry and reflection conditions in reciprocal space

Paolo G. Radaelli

in Symmetry in Crystallography: Understanding the International Tables

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199550654
eISBN:
9780191775093
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550654.003.0011
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

This chapter focuses on symmetry in reciprocal space. It reviews the definitions of reciprocal space and dual (reciprocal) basis vectors (from Chapter 6), and presents the new concept of the ... More


Lattices

Mark Ladd

in Symmetry of Crystals and Molecules

Published in print:
2014
Published Online:
April 2014
ISBN:
9780199670888
eISBN:
9780191781124
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670888.003.0004
Subject:
Physics, Crystallography: Physics

The definition of ‘lattice’ in one, two, and three dimensions is discussed, together with the choice of unit cell. The Bravais lattices are explained with stereoscopic illustrations, system by ... More


Diffraction in the Static Approximation

Andrew T. Boothroyd

in Principles of Neutron Scattering from Condensed Matter

Published in print:
2020
Published Online:
October 2020
ISBN:
9780198862314
eISBN:
9780191895081
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198862314.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics, Condensed Matter Physics / Materials

The basic principles of crystallography are reviewed, including the lattice, basis and reciprocal lattice. The Bragg diffraction law and Laue equation, which describe coherent scattering from a ... More


Crystallography and Diffraction

Kannan M. Krishnan

in Principles of Materials Characterization and Metrology

Published in print:
2021
Published Online:
July 2021
ISBN:
9780198830252
eISBN:
9780191868665
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198830252.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

Crystalline materials have a periodic arrangement of atoms, exhibit long range order, and are described in terms of 14 Bravais lattices, 7 crystal systems, 32 point groups, and 230 space groups, as ... More


Bulk and thin film organic crystal structures

Stephen R. Forrest

in Organic Electronics: Foundations to Applications

Published in print:
2020
Published Online:
October 2020
ISBN:
9780198529729
eISBN:
9780191798238
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198529729.003.0002
Subject:
Physics, Condensed Matter Physics / Materials, Crystallography: Physics

Organic electronic devices are comprised of materials that are amorphous, nanocrystalline, microcrystalline, or single crystalline solids bonded by weak van der Waals forces. This chapter presents ... More


X-ray diffraction: the contributions of Max von Laue, W. H. and W. L. Bragg and P. P. Ewald

Christopher Hammond

in The Basics of Crystallography and Diffraction

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198738671
eISBN:
9780191801938
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198738671.003.0008
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

The chapter starts with an historical introduction to the topics covered here. It describes Laue's analysis of X-ray diffraction, i.e. how to derive the three Laue equations. It moves on to provide ... More


Phonons

Ian R. Kenyon

in Quantum 20/20: Fundamentals, Entanglement, Gauge Fields, Condensates and Topology

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198808350
eISBN:
9780191846052
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198808350.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

Phonons are introduced as an example of quasi-particles that can only exist in matter. Debye’s quantum model for heat capacity of solids and comparison with experimentin different temperature ranges ... More


Fundamentals of crystallography

Carmelo Giacovazzo

in Phasing in Crystallography: A Modern Perspective

Published in print:
2013
Published Online:
November 2020
ISBN:
9780199686995
eISBN:
9780191918377
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199686995.003.0006
Subject:
Chemistry, Crystallography: Chemistry

In this chapter we summarize the basic concepts, formulas and tables which constitute the essence of general crystallography. In Sections 1.2 to 1.5 we recall, without examples, definitions for ... More


An Executable Notation, with Illustrations from Elementary Crystallography

Donald B. Mclntyre

in Computers in Geology - 25 Years of Progress

Published in print:
1994
Published Online:
November 2020
ISBN:
9780195085938
eISBN:
9780197560525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195085938.003.0024
Subject:
Computer Science, Software Engineering

Elementary crystallography is an ideal context for introducing students to mathematical geology. Students meet crystallography early because rocks are made of crystalline minerals. Moreover, ... More


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